A credit score is used by credit agencies​ (such as mortgagecompanies and​ banks) to assess the creditworthiness ofindividuals. Values range from 300 to​ 850, with a credit scoreover 700 considered to be a quality credit risk. According to a​survey, the mean credit score is 705.9. A credit analyst wonderedwhether​ high-income individuals​ (incomes in excess of​ $100,000per​ year) had higher credit scores. He obtained a random sample of39 ​high-income individuals and found the sample mean credit scoreto be 718.1 with a standard deviation of 81.7. Conduct theappropriate test to determine if​ high-income individuals havehigher credit scores at the alphaequals0.05 level of significance.State the null and alternative hypotheses. Upper H 0​: mu ▼ lessthan not equals equals greater than nothing Upper H 1​: mu ▼ notequals less than greater than equals nothing ​(Type integers ordecimals. Do not​ round.) Identify the​ t-statistic. t 0equalsnothing ​(Round to two decimal places as​ needed.) Identify the​P-value. ​P-valueequals nothing ​(Round to three decimal places as​needed.) Make a conclusion regarding the hypothesis. ▼ Reject Failto reject the null hypothesis. There ▼ is is not sufficientevidence to claim that the mean credit score of​ high-incomeindividuals is ▼ less than equal to greater than nothing.
